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Question

A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

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Solution

Given,

Distance =360 km
Let the speed be x, then time taken

t=360x
If speed is increased by 5 km/h speed will be (x+5)km/h
Distance is the same
t=360(x+5)

time with original speed - time with increased speed =1
therefore,
360x360(x+5)=1
LCM=x(x+5)
Hence,

360(x+5)360xx(x+5)=1
360x+1800360x=x(x+5)
x2+5x=1800
x2+5x1800=0
x2+45x40x1800=0
x(x+45)40(x+45)=0
(x40)(x+45)=0
x=40 kmhr,

So the speed of the train is 40 km/hr. We have discarded the other value as the negative value of speed (45) is not possible.


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